id: 06592123
dt: b
an: 2016e.00798
au: Klein, Felix
ti: Elementary mathematics from a higher standpoint. Volume III: precision
mathematics and approximation mathematics. Translated from the 3rd
German edition by Marta Menghini and Anna Baccaglini-Frank.
Mathematical advisor for the English translation: Gerd Schubring.
so: Berlin: Springer (ISBN 978-3-662-49437-0/pbk; 978-3-662-49439-4/ebook;
978-3-662-49515-5/set). xviii, 259~p. (2016).
py: 2016
pu: Berlin: Springer
la: EN
cc: I10 G10
ut:
ci: Zbl 1341.11001; Zbl 1341.51001; JFM 54.0068.03
li: doi:10.1007/978-3-662-49439-4
ab: Publisher’s description: These three volumes constitute the first
complete English translation of Felix Klein’s seminal series
“Elementarmathematik vom höheren Standpunkte aus". “Complete" has
a twofold meaning here: First, there now exists a translation of Volume
III into English, while until today the only translation had been into
Chinese. Second, the English versions of Volume I and II had omitted
several, even extended parts of the original, while we now present a
complete revised translation into modern English. The volumes, first
published between 1902 and 1908, are lecture notes of courses that
Klein offered to future mathematics teachers, realizing a new form of
teacher training that remained valid and effective until today: Klein
leads the students to gain a more comprehensive and methodological
point of view on school mathematics. The volumes enable us to
understand Klein’s far-reaching conception of elementarisation, of
the “elementary from a higher standpoint", in its implementation for
school mathematics. In Volume III, Klein explores the relationship
between precision and approximation mathematics. He crosses the various
fields of mathematics ‒ from functions in one and two variables to
practical geometry to space curves and surfaces ‒ underlining the
relation between the exactness of the idealised concepts and the
approximations to be considered in applications. Logical procedures are
confronted with the way in which concepts arise starting from
observations. It is a comparison between properties pertaining only to
the theoretical field of abstract mathematics and properties that can
be grasped by intuition. The final part, which concerns gestalt
relations of curves and surfaces, shows Klein to be the master of the
art of description of geometric forms. For Volumes I and II see [Zbl
1341.11001; Zbl 1341.51001]. For the original 3rd German edition see
[JFM 54.0068.03]
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